(See attachment please) What postulate can be used to prove that △ADC≅△CBA ?

Mathematics

1 answer:

e-lub [12.9K]3 years ago

5 0

The postulate you can use to prove that those triangles are congruent is the SSS. Since BC and AD are congruent (given), AB and DC are congruent (given), and AC and AC are congruent (i forgot which postulate it is, however, it states that the same line is congruent with itself)

hope this helps

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Can you tell me how to factorise 6b+24bc

Kamila [148]

When we factorise an expression, we are looking for simple factors that multiply to get the original expression. Usually it is very natural to factorise something like a quadratic in x. For example:

x^2 + 3x + 2 = (x+1)(x+2)

But there are other situations where factorisation can be applied. Take this quadratic:

x^2 - 9x = x(x-9)

This second example is closer to the question in hand. Just like x was a common factor to both x^2 and -9x, we are looking for a common factor to both 6b and 24bc. The common factor is 6b.

Hence 6b + 24bc = 6b(1 + 4c).

I hope this helps you :)

3 0

3 years ago

Read 2 more answers

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet

abruzzese [7]

Answer:

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes

Step-by-step explanation:

The given parameters are;

The diameter of the balloon = 55 feet

The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute

We have;

dr/dt = 1.5 feet per minute = 1.5 ft/min

V = 4/3·π·r³

The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³

When the volume is two-thirds the maximum volume, we have;

2/3 × 696556.67 ft³ = 464371.11 ft³

The value of the radius, r₂ at that point is found as follows;

4/3·π·r₂³ = 464371.11 ft³

r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³

348278.333333

r₂ = ∛(348278.33 ft³) ≈ 70.36 ft

The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)

The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.

4 0

3 years ago

Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must

Readme [11.4K]

Answer:

The number of ways is 26,400 ways

Step-by-step explanation:

Given;

total number of men, M = 10

total number of women, W = 12

number of committees to be formed = 6

If there must be equal gender, then it must consist of 3 men and 3 women.

$The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways$